login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A364230 Triangle read by rows: T(n, k) is the number of n X n symmetric Toeplitz matrices of rank k using all the integers 1, 2, ..., n. 1
1, 0, 2, 0, 0, 6, 0, 0, 0, 24, 0, 0, 0, 0, 120, 0, 0, 0, 0, 2, 718, 0, 0, 0, 0, 4, 31, 5005, 0, 0, 0, 0, 0, 2, 44, 40274, 0, 0, 0, 0, 0, 0, 4, 272, 362604, 0, 0, 0, 0, 0, 0, 0, 111, 774, 3627915, 0, 0, 0, 0, 0, 0, 2, 14, 244, 6974, 39909566, 0, 0, 0, 0, 0, 0, 0, 4, 64, 743, 9533, 478991256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Wikipedia, Toeplitz Matrix
EXAMPLE
The triangle begins:
1;
0, 2;
0, 0, 6;
0, 0, 0, 24;
0, 0, 0, 0, 120;
0, 0, 0, 0, 2, 718;
0, 0, 0, 0, 4, 31, 5005;
...
MATHEMATICA
T[n_, k_]:= Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Range[n]], i]]], {i, n!}], k]; Table[T[n, k], {n, 8}, {k, n}]//Flatten
PROG
(PARI)
MkMat(v)={matrix(#v, #v, i, j, v[1+abs(i-j)])}
row(n)={my(f=vector(n)); forperm(vector(n, i, i), v, f[matrank(MkMat(v))]++); f} \\ Andrew Howroyd, Dec 30 2023
CROSSREFS
Cf. A000142 (row sums), A350953 (minimal determinant), A350954 (maximal determinant), A351019 (minimal permanent), A351020 (maximal permanent), A356865 (minimal nonzero absolute value determinant), A364231 (right diagonal).
Sequence in context: A106512 A181229 A364233 * A259857 A364790 A094785
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jul 14 2023
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Dec 30 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 20:49 EDT 2024. Contains 374323 sequences. (Running on oeis4.)